Heirarchical Multivariate Modeling?
On Tue, 23 Sep 2008, Ken Beath wrote:
On 19/09/2008, at 8:41 AM, Adam D. I. Kramer wrote:
Dear colleagues, My actual interest is in 1. estimating an aggregate PCA based on the factor structures that exist within many individuals, each of which is based on a different number of observations among the same set of variables, and 2. testing whether factor structures differ across people (e.g., whether prediction improves if I model a random effect for subject). This can be thought of as adding and testing a random effect to a PCA, or something similar.
It is possible to create multilevel versions of multivariate methods, maybe not PCA, but for factor analysis, yes. The sem package could probably be coerced into fitting them for linear models, otherwise the commercial programs Latent Gold and MPlus are the only solutions. The Mplus site has lots of modelling info. Ken
What he said ;) Look at any textbook on structural equation modelling under measurement model etc. If you have binary or ordinal data, we fit multivariate random effects models under the threshold model (see tetrachoric or polychoric correlations), usually these days with Mx (http://www.vcu.edu/mx/). Mx can fit to summary correlation or covariance matrices, but also implements "raw data" ML methods that would deal with varying numbers and types of observations per individual such as you describe. David Duffy.
| David Duffy (MBBS PhD) ,-_|\ | email: davidD at qimr.edu.au ph: INT+61+7+3362-0217 fax: -0101 / * | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v